Sixuan Lou : Jumping lines and conics

Posted by Sixuan Lou , part of the Graduate Algebraic Geometry Seminar.

At

April 17, 2023, 4 p.m.

In

427 SEO

Abstract

Given a stable vector bundle on a projective variety, it is natural to ask what it looks like when we restrict to a complete intersection subvariety. The theorem of Grauert and Mülich gives us a numerical constraint for the Harder-Narasimhan filtration of the restricted bundle on a general such complete intersection. On the other hand, one can ask what the locus of complete intersections on which our bundle exhibit non-generic filtration looks like. In this talk we will investigate this question in the simplest setting of restriction to lines in P^2 and conic sections on a smooth quadric.